The Frobenius problem, rational polytopes, and Fourier-Dedekind Sums

Matthias Beck, Ricardo Diaz, Sinai Robins

We study the number of lattice points in integer dilates of the rational polytope $P=(x_1,...,x_n)\in {\mathbb{R}}_{\ge 0}^n:{\sum }_{k=1}^n{x}_k{a}_k\le 1$, where $a_1,...,a_n$ are posit…